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Fractional model equation for anomalous diffusion

Citations

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Cited by:

  1. Afzaal Mubashir Hayat & Muhammad Bilal Riaz & Muhammad Abbas & Moataz Alosaimi & Adil Jhangeer & Tahir Nazir, 2024. "Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function," Mathematics, MDPI, vol. 12(13), pages 1-22, July.
  2. Liu, Ting & Li, Guohua & Zhang, Hong & Huang, Xiangwen & Wang, Xiaoxuan & Tang, Xiaoyu & Tu, Zeyu, 2025. "Lévy walk with asymmetric walking times in complex environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 679(C).
  3. Claudia A. Pérez-Pinacho & Cristina Verde, 2022. "A Note on an Integral Transformation for the Equivalence between a Fractional and Integer Order Diffusion Model," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
  4. Rui, Weiguo, 2018. "Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 158-171.
  5. Min, Seungsik & Shin, Ki-Hong & Baek, Woonhak & Kim, Kyungsik & You, Cheol-Hwan & Lee, Dong-In & Yum, Seong Soo & Kim, Wonheung & Chang, Ki-Ho, 2020. "Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
  6. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
  7. Vyacheslav Svetukhin, 2021. "Nucleation Controlled by Non-Fickian Fractional Diffusion," Mathematics, MDPI, vol. 9(7), pages 1-11, March.
  8. Dmitry Zhukov & Konstantin Otradnov & Vladimir Kalinin, 2024. "Fractional-Differential Models of the Time Series Evolution of Socio-Dynamic Processes with Possible Self-Organization and Memory," Mathematics, MDPI, vol. 12(3), pages 1-19, February.
  9. Essex, Christopher & Schulzky, Christian & Franz, Astrid & Hoffmann, Karl Heinz, 2000. "Tsallis and Rényi entropies in fractional diffusion and entropy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 299-308.
  10. Satin, Seema E. & Parvate, Abhay & Gangal, A.D., 2013. "Fokker–Planck equation on fractal curves," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 30-35.
  11. Viacheslav V. Saenko & Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Ekaterina V. Tsvetova, 2022. "Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method," Mathematics, MDPI, vol. 10(3), pages 1-19, February.
  12. Lenzi, E.K. & Mendes, R.S. & Gonçalves, G. & Lenzi, M.K. & da Silva, L.R., 2006. "Fractional diffusion equation and Green function approach: Exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 215-226.
  13. Fernando Alcántara-López & Carlos Fuentes & Rodolfo G. Camacho-Velázquez & Fernando Brambila-Paz & Carlos Chávez, 2022. "Spatial Fractional Darcy’s Law on the Diffusion Equation with a Fractional Time Derivative in Single-Porosity Naturally Fractured Reservoirs," Energies, MDPI, vol. 15(13), pages 1-11, July.
  14. Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
  15. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
  16. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.
  17. Saenko, Viacheslav V., 2016. "The influence of the finite velocity on spatial distribution of particles in the frame of Levy walk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 765-782.
  18. Lenzi, M.K. & Lenzi, E.K. & Guilherme, L.M.S. & Evangelista, L.R. & Ribeiro, H.V., 2022. "Transient anomalous diffusion in heterogeneous media with stochastic resetting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
  19. Razminia, Kambiz & Razminia, Abolhassan & Torres, Delfim F.M., 2015. "Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 374-380.
  20. Roscani, Sabrina D. & Bollati, Julieta & Tarzia, Domingo A., 2018. "A new mathematical formulation for a phase change problem with a memory flux," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 340-347.
  21. Paradisi, Paolo & Cesari, Rita & Mainardi, Francesco & Tampieri, Francesco, 2001. "The fractional Fick's law for non-local transport processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 130-142.
  22. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
  23. Krasowska, Monika & Strzelewicz, Anna & Rybak, Aleksandra & Dudek, Gabriela & Cieśla, Michał, 2016. "Structure and transport properties of ethylcellulose membranes with different types and granulation of magnetic powder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 241-250.
  24. Huang, Jianping & Zhou, Huacheng, 2026. "Causal state feedback representation for infinite horizon LQ problems of fractional systems," Applied Mathematics and Computation, Elsevier, vol. 510(C).
  25. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.
  26. Hu, Xiuling & Liao, Hong-Lin & Liu, F. & Turner, I., 2015. "A center Box method for radially symmetric solution of fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 467-486.
  27. Dmitry Zhukov & Vadim Zhmud & Konstantin Otradnov & Vladimir Kalinin, 2024. "Solution of Fractional Differential Boundary Value Problems with Arbitrary Values of Derivative Orders for Time Series Analysis," Mathematics, MDPI, vol. 12(24), pages 1-24, December.
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